14 



PROFESSOR CARGILL G. KNOTT ON 



From Table I. we may readily calculate that these corresponding pairs of magnetising 

 forces give for the ratios of the inductions 



•939, -914, -957 



respectively. These are all somewhat higher than the experimental values just given. 

 This, however, is not surprising inasmuch as the kinds of iron composing the two tubes 

 may differ enough to render the numbers in Table I. not strictly applicable to the b tube. 

 And, again, the theory itself that is made use of in estimating the average magnetic force 

 and the induction due thereto is admittedly only approximately true. The comparison 

 just made seems to show that it is nevertheless a tolerably fair approximation to the 

 truth.. 



The ratios of the sectional and axial inductions call next for consideration. At a 

 glance we see that the ratios given in Table II. are all less than the corresponding 

 multipliers in equations E. This means that // is less than /x in every instance. In a 

 general way, it is easy to see that this ought to be so. The fields due to axial and 

 sectional currents of the same strength, although they are the same in the region outside 

 the tube, have quite different values in the substance of the tube. The field due to the 

 axial current increases as we pass inwards to the interior surface ; while that due to the 

 sectional current diminishes, and has the value zero at the interior surface. In any case, 

 we may estimate the average field by dividing the total normal induction by the radial 

 section. The values of the average fields, so estimated for the different tubes, are 

 shown in the following table : — 





Average Field due to Current 





Tube. 











•49 



1-05 2 



09 



A 



•1058 



•2268 



4514 



A' 



•0353 



•0756 



1503 



B 



•1049 



•2247 



4473 



B' 



•0350 



■0749 



1491 



a 



•0785 



•1682 



3348 



a' 



•0342 



•0732 



1457 



b 



•0782 



•1675 



3333 



V 



0341 



•0731 



1455 



Now each of these fields has its appropriate permeability ; and by means of Table I. 

 we may calculate the permeabilities in the case of Tube A. From Table II. we see that 

 Tube B behaves very similarly to Tube A ; and that Tube a, notwithstanding the fact 

 that the permeability of its material is comparatively small, behaves almost exactly like 

 Tube b. This is significant as showing that the relation between the sectional and axial 

 inductions is largely independent of the numerical values of the permeabilities involved. 

 Hence we may reasonably discuss the case of the Tubes a and b by applying to them 

 the results of Table I. In this discussion we shall take the means of the various values 



